Safety Control Method and System for Two-Wheeled Robots Against Periodic Markov DoS Attacks

Abstract

This disclosure provides a method and system for safe control of two-wheeled robots against periodic Markov DoS attacks, relating to the field of robot safety control technology. The method includes: constructing a kinematic model of the two-wheeled robot; integrating and fusing the kinematic model and system signals through a communication network to construct a networked two-wheeled robot control system (NCSs); linearizing and discretizing the NCSs to obtain a discrete-time linear state-space model, and constructing the motion target of the two-wheeled robot; determining the attack type; using switched system theory to transform the attacked NCSs into a cyclic Markov system with modal dwell time; setting a controller; calculating the control gain based on the subsystem constraints of the switched system to control the two-wheeled robot; tracking the target trajectory of the two-wheeled robot; and achieving safe control of the networked two-wheeled robot system against periodic Markov DoS attacks.

Description

Technical Field

[0001] This disclosure relates to the field of robot safety control technology, specifically to a two-wheeled robot safety control method and system for dealing with periodic Markov DoS attacks. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] With the increasing maturity of communication networks, networked control systems (NCSs), which integrate physical systems with computers through actuators, sensors, and communication networks, have developed rapidly. To date, NCSs have been widely applied in various fields such as autonomous driving, aerospace, and smart grids. Two-wheeled robots, controlled by computers via wireless communication networks and feeding information back to the computer through sensors, also fall under the category of NCSs. However, while the openness of communication networks improves efficiency and convenience, it also increases the threat of malicious attacks on NCSs. Based on the attack method, the main threats are spoofing attacks and denial-of-service (DoS) attacks. The former harms NCSs by intercepting, modifying, and injecting transmission signals, while the latter causes significant performance degradation by inducing communication channel delays and signal loss.

[0004] From the perspective of traditional two-wheeled robot control, developing accurate attack models is crucial for both defense and attack. In recent years, periodic DoS attacks have attracted widespread attention in both industry and academia due to their destructiveness and ease of implementation, such as low-rate DoS attacks in the TCP protocol. However, the fixed initiation patterns of periodic attacks are easily identified and defended against by NCSs (Neural Control System). Therefore, such attacks launched randomly are more attractive to attackers due to their high flexibility. In this context, Bernoulli DoS attacks and Markov DoS attacks can be considered special cases with a single period.

[0005] In recent years, NCSs subjected to DoS attacks have often been modeled as switching systems consisting of stable (silent attacks) and unstable (active attacks) subsystems. It is noteworthy that the stability of the subsystems and the switching system is rarely directly correlated. Even if all subsystems are stable, the closed-loop system can still diverge if the switching rules are not applied correctly. Therefore, transforming DoS-attacked NCSs into switching systems and ensuring the robustness of the system without switching constraints remains challenging. Summary of the Invention

[0006] To address the aforementioned issues, this disclosure proposes a safety control method and system for two-wheeled robots resistant to periodic Markov DoS attacks. It establishes a discrete linearized state-space expression for the networked two-wheeled robot. Based on switching system theory, the system modes under (without) attacks can be considered as unstable (stable) sub-modes of a switching system, thus transforming the networked two-wheeled robot system under DoS attacks into a cyclic Markov switching system with MDT. The proposed method eliminates the need for additional switching signal constraints, effectively reducing the design complexity of the safety control algorithm.

[0007] According to some embodiments, the present disclosure adopts the following technical solutions:

[0008] A two-wheeled robot safety control method for periodic Markov DoS attacks includes:

[0009] A kinematic model of a two-wheeled robot is constructed, and the kinematic model and system signals of the two-wheeled robot are integrated and fused through a communication network to construct a networked two-wheeled robot control system (NCSs).

[0010] The networked two-wheeled robot control system (NCSs) is linearized and discretized to obtain a discrete-time linear state-space model, and the motion target of the two-wheeled robot is constructed.

[0011] By identifying the type of attack, and using switching system theory, the networked two-wheeled robot control system (NCSs) under attack is transformed into a cyclic Markov system with modal dwell time. A controller is set up, and based on the subsystem constraints of the switching system, its control gain is calculated to control the two-wheeled robot and track the target trajectory of the two-wheeled robot, thus achieving safe control of the networked two-wheeled robot system subjected to periodic Markov DoS attacks.

[0012] According to some embodiments, the present disclosure adopts the following technical solutions:

[0013] A safety control system for two-wheeled robots designed to withstand periodic Markov DoS attacks includes:

[0014] The system construction module is used to build a kinematic model of a two-wheeled robot. It integrates and fuses the kinematic model and system signals of the two-wheeled robot through a communication network to build a networked two-wheeled robot control system (NCSs).

[0015] The linearization and discretization module is used to linearize and discretize the networked two-wheeled robot control system (NCSs) to obtain a discrete-time linear state-space model and construct the motion target of the two-wheeled robot.

[0016] The security control module is used to determine the type of attack. Utilizing switching system theory, the networked two-wheeled robot control system (NCSs) under attack is transformed into a cyclic Markov system with modal dwell time. A controller is set up, and based on the subsystem constraints of the switching system, its control gain is calculated to control the two-wheeled robot and track the target trajectory of the two-wheeled robot, thereby achieving security control of the networked two-wheeled robot system subjected to periodic Markov DoS attacks.

[0017] According to some embodiments, the present disclosure adopts the following technical solutions:

[0018] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned two-wheeled robot safety control method against periodic Markov DoS attacks.

[0019] According to some embodiments, the present disclosure adopts the following technical solutions:

[0020] An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the two-wheeled robot safety control method for periodic Markov DoS attacks.

[0021] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0022] This paper discloses a safety control method for two-wheeled robots against periodic Markov DoS attacks. It investigates the safety control of two-wheeled robots under a periodic Denial-of-Service (DoS) attack exhibiting Markov characteristics. First, signals from the two-wheeled robot and computer are fused using a communication network to form a networked two-wheeled robot control system (NCSs). Its dynamic mathematical model is constructed, and the continuous system is discretized to obtain a discrete-time state-space model. Second, using switching system theory, the attacked NCSs are transformed into a cyclic Markov system with modal dwell time (MTD). This novel safety control method requires only subsystem constraints and not switching constraints. Experiments with this networked two-wheeled robot verify the practicality, efficiency, and superiority of the proposed method.

[0023] This disclosed method for safety control of two-wheeled robots against periodic Markov DoS attacks considers a more general and practical form of periodic Markov DoS attack compared to traditional periodic DoS attacks and Markov DoS attacks. Based on MDT, it transforms the attacked NCSs into a cyclic Markov system, and is an innovative safety control method that relies only on subsystem constraints without switching constraints. This method significantly improves robustness compared to existing robustness analysis based on switching constraints.

[0024] This paper discloses a novel safety control method for two-wheeled robots facing periodic Markov DoS attacks. Based on switching system theory and MDT constraints, the method proposes a novel safety control approach. First, a discrete linearized state-space expression for the networked two-wheeled robot is established. Based on switching system theory, the system modes under (without) attacks can be considered as unstable (stable) sub-modes of the switching system, thus transforming the networked two-wheeled robot system under DoS attacks into a cyclic Markov switching system with MDT. On this basis, a safety control method for the MDT constraints of the switching subsystem is proposed. Compared with traditional methods, the proposed method does not require additional switching signal constraints, effectively reducing the design complexity of the safety control algorithm. Finally, trajectory tracking experiments on the two-wheeled robot verify the practicality and efficiency of the proposed method.

[0025] This paper discloses a two-wheeled robot safety control method for periodic Markov DoS attacks. Utilizing switched system theory, it transforms the attacked NCSs (Neural System Classes) into cyclic Markov systems with modal dwell time (MTD). Compared to existing robustness analyses based on switching rules, this method relies only on subsystem constraints, eliminating the need for switching constraints. Experiments with a two-wheeled robot validate the effectiveness, efficiency, and state-of-the-art nature of the proposed method. Attached Figure Description

[0026] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0027] Figure 1 This is an example of a networked two-wheeled robot system architecture under periodic Markov DoS attacks according to an embodiment of this disclosure.

[0028] Figure 2 This is a schematic diagram of a periodic Markov DoS attack according to an embodiment of the present disclosure;

[0029] Figure 3 The actual and reference trajectories of the robot without computer control according to embodiments of this disclosure;

[0030] Figure 4 This is the state trajectory of the error system (1) under a DoS attack according to an embodiment of this disclosure;

[0031] Figure 5 The state trajectory of the error system (1) under a DoS attack in this embodiment of the present disclosure is the running trajectory of the lateral, longitudinal and yaw angle errors of the two-wheeled robot under a DoS attack.

[0032] Figure 6 The reference trajectory and actual running trajectory of the two-wheeled robot under a DoS attack are shown in this embodiment of the present disclosure. Detailed Implementation

[0033] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0034] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0035] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0036] Example 1

[0037] One embodiment of this disclosure provides a safety control method for a two-wheeled robot against periodic Markov DoS attacks, including:

[0038] Step 1: Construct a kinematic model of the two-wheeled robot, and integrate the kinematic model and system signals of the two-wheeled robot through a communication network to construct a networked two-wheeled robot control system (NCSs).

[0039] Step 2: Linearize and discretize the networked two-wheeled robot control system (NCSs) to obtain a discrete-time linear state-space model, and construct the motion target of the two-wheeled robot;

[0040] Step 3: Determine the type of attack. Using the switching system theory, transform the attacked networked two-wheeled robot control system (NCSs) into a cyclic Markov system with modal dwell time. Set up a controller and calculate its control gain based on the subsystem constraints of the switching system to control the two-wheeled robot and track the target trajectory of the two-wheeled robot, thus achieving safe control of the networked two-wheeled robot system subjected to periodic Markov DoS attacks.

[0041] As one embodiment, this disclosure presents a two-wheeled robot security control method for periodic Markov DoS attacks. The method investigates the security control of a two-wheeled robot under a denial-of-service (DoS) attack exhibiting Markov characteristics and occurring periodically. The specific implementation process is as follows:

[0042] Step 1: Networked Two-Wheeled Robot Model

[0043] Specifically, the two-wheeled mobile robot is controlled by a computer via a wireless communication network, and sensors feed information back to the computer, thereby forming... Figure 1 The networked two-wheeled robot control system (NCSs) is shown. The robot's behavior can be represented by vectors. ,in Indicates coordinate position, Indicates the heading angle.

[0044] The kinematic model of the robot is described as follows:

[0045]

[0046] in and These represent the robot's linear velocity and angular velocity, respectively. This indicates a disturbance, which may be caused by various factors, such as insufficient precision of the actuator causing the actual speed of the vehicle to be different from the given speed input; or uneven road surface or insufficient friction causing the vehicle to slip.

[0047] The robot's goal is to track the following circular trajectory:

[0048] ,

[0049] in It is the parameter vector of the target trajectory.

[0050] To obtain the tracking error system, let:

[0051]

[0052] Accordingly, let the sampling period be... By linearizing and discretizing, the following discrete-time state-space model can be obtained:

[0053] (1)

[0054] in,

[0055]

[0056] in, It is the system status; It is a control input; It controls the output. It's interference. It is a given constant. and They represent the set of real numbers and the set of natural numbers, respectively.

[0057] Step 2: Construct a periodic Markov DoS attack model to determine the type of attack;

[0058] Specifically, in networked two-wheeled robot control systems (NCSs), the vulnerability of the wireless network makes the control channel susceptible to malicious DoS attacks. The duration of a single non-attack is defined as follows: The duration of a single DoS attack is Then define For time The model indicator at that time. Therefore, the DoS attack indicator can be described as follows:

[0059]

[0060] For example, let , ,but For each , , and The relationship between them is as follows Figure 2 As shown.

[0061] Consider the Markov transition probabilities (MTPs) under different modes as follows:

[0062]

[0063] in .

[0064] If the transition probability If so, it is a cyclical DoS attack; if This would be a Markov DoS attack.

[0065] Step 3: Using switching system theory, the networked two-wheeled robot control system NCSs under attack is transformed into a cyclic Markov system with modal dwell time, thereby achieving safe control of the two-wheeled robot.

[0066] The controller can be designed as follows:

[0067]

[0068] Therefore, the original system can be transformed into a switching system in the following form:

[0069] (2)

[0070] The derivation process is as follows, including the formulation of assumptions and definitions.

[0071] Assumption 1: It is measurable;

[0072] Assumption 2: It is controllable;

[0073] Definition 1: For any ,make( ) indicates in The number of subsystem switches under non-attack (attack) conditions. Indicates in Total dwell time of the subsystem under non-attack (attack) conditions. If there is... , so that

[0074]

[0075] but ( This is called the modal residence time (MDT) of the stable (unstable) switching subsystem.

[0076] Definition 2: For If it satisfies:

[0077] 1) For And each Yes, they all are.

[0078]

[0079] 2) For And with zero initial conditions, we have

[0080]

[0081] Then formula (1) is called having Stochastic stability of performance metrics.

[0082] This section addresses the security control problem of NCSs under DoS attacks by addressing subsystem constraints based on switching systems. Unlike previous studies that required both subsystem and switching constraints to be satisfied simultaneously, this section focuses on requiring only subsystem constraints, eliminating the need for switching constraints. Sufficient conditions for NCSs security are then derived.

[0083] Theorem: For a given real number If a matrix exists and positive definite matrix , so that

[0084] (3)

[0085] (4)

[0086] (5)

[0087] in, Then system (1) has The stochastic stability of the performance index, where A, B, C, and D are the coefficient matrices in formula (1), It is the identity matrix;

[0088] In addition, controller gain can be obtained in the following ways. :

[0089]

[0090] Proof: Let This is the switching time.

[0091] for Consider the following Lyapunov function:

[0092]

[0093] for If the conditions are met,

[0094] ,

[0095] Then the following formula holds true.

[0096]

[0097] for If the conditions are met,

[0098] ,

[0099] Then the following formula holds true.

[0100]

[0101] because Then the following two equations also hold true.

[0102] .

[0103] for The following formula holds true.

[0104]

[0105] in .

[0106] for The following formula holds true.

[0107]

[0108] in .

[0109] Note that for (3)-(4) meet the conditions .

[0110] Therefore, for ,have,

[0111]

[0112] When condition (5) is satisfied, system (1) is stochastically stable.

[0113] for ,make .remember This is the switching time. If the above formulas (3)-(4) hold true,

[0114] Using Schul's complement lemma, the following inequality can be derived:

[0115] for ,have,

[0116]

[0117] in .

[0118] for ,have,

[0119]

[0120] for ,have,

[0121]

[0122] in .

[0123] for ,have,

[0124]

[0125] in .

[0126] because ,have,

[0127]

[0128] from Iteration to ,get,

[0129]

[0130] Under zero initial conditions, we have and Then there is,

[0131]

[0132] make ,have,

[0133]

[0134] By combining the transformation of double summation and the limit calculation of geometric series, the following formula can be derived:

[0135]

[0136] Therefore, according to definition 1, system (1) is realized with Stochastic stability of performance metrics.

[0137] For subsequent simulations and experiments, the initial parameters are selected as follows: , ,as well as Then system (1) can be written as

[0138]

[0139] Without a controller applied, the robot's actual trajectory and reference trajectory are as follows: Figure 3 As shown, without a controller, the robot cannot track the target trajectory.

[0140] make Using Theorem 1, we can calculate... .

[0141] By solving the linear matrix inequalities (LMI) of equations (3)-(4), the control gain is obtained as follows:

[0142]

[0143] The state trajectory diagram of error system (1) is as follows: Figure 4 As shown in the image, the gray area represents the time period during which the DoS attack was launched. It can be seen that the tracking error can quickly converge to... That is, to achieve under periodic Markov DoS attacks and external interference. Stochastic stability of performance metrics.

[0144] Furthermore, in actual experiments, the trajectory diagrams of the robot's lateral, longitudinal, and yaw angle errors are as follows: Figure 5 As shown. The robot's actual and tracking trajectories are also as follows. Figure 6 As shown, the robot can perfectly track the target trajectory.

[0145] Example 2

[0146] One embodiment of this disclosure provides a safety control system for a two-wheeled robot against periodic Markov DoS attacks, including:

[0147] The system construction module is used to build a kinematic model of a two-wheeled robot. It integrates and fuses the kinematic model and system signals of the two-wheeled robot through a communication network to build a networked two-wheeled robot control system (NCSs).

[0148] The linearization and discretization module is used to linearize and discretize the networked two-wheeled robot control system (NCSs) to obtain a discrete-time linear state-space model and construct the motion target of the two-wheeled robot.

[0149] The security control module is used to determine the type of attack. Utilizing switching system theory, the networked two-wheeled robot control system (NCSs) under attack is transformed into a cyclic Markov system with modal dwell time. A controller is set up, and based on the subsystem constraints of the switching system, its control gain is calculated to control the two-wheeled robot and track the target trajectory of the two-wheeled robot, thereby achieving security control of the networked two-wheeled robot system subjected to periodic Markov DoS attacks.

[0150] Example 3

[0151] One embodiment of this disclosure provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the aforementioned two-wheeled robot safety control method against periodic Markov DoS attacks.

[0152] Example 4

[0153] One embodiment of this disclosure provides an electronic device comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the two-wheeled robot safety control method for periodic Markov DoS attacks.

[0154] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0155] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0156] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A safety control method for a two-wheeled robot against periodic Markov DoS attacks, characterized in that, include: A kinematic model of a two-wheeled robot is constructed, and the kinematic model and system signals of the two-wheeled robot are integrated and fused through a communication network to construct a networked two-wheeled robot control system (NCSs). The networked two-wheeled robot control system (NCSs) is linearized and discretized to obtain a discrete-time linear state-space model, and the motion target of the two-wheeled robot is constructed. The attack type is determined, and the networked two-wheeled robot control system (NCSs) under attack is transformed into a cyclic Markov system with modal dwell time using switching system theory. A controller is set up, and its control gain is calculated based on the subsystem constraints of the switching system to control the two-wheeled robot and track the target trajectory of the two-wheeled robot, thereby realizing the safe control of the networked two-wheeled robot system under periodic Markov DoS attacks. In networked two-wheeled robot control systems (NCSs), the vulnerability of the wireless network makes the control channel susceptible to malicious DoS attacks. The duration of a single non-attack is defined as follows: The duration of a single DoS attack is , Let the set of natural numbers be defined. For time The model indicator for DoS attacks is described as follows: Consider the Markov transition probabilities (MTPs) under different modes as follows: in ; Therefore, the following controller is designed: ， K For controller gain; transform the attacked NCSs into cyclic Markov systems with modal dwell times: ； The system mode under attack is regarded as an unstable sub-mode of the switching system, thus transforming the networked two-wheeled robot system under DoS attack into a cyclic Markov switching system with MDT, without the need to impose additional switching signal constraints. in It is the system status; It controls the output. It's interference. It is the set of real numbers; They are all coefficient matrices of the corresponding dimensions.

2. The two-wheeled robot safety control method for periodic Markov DoS attacks as described in claim 1, characterized in that, The two-wheeled robot is controlled by a controller system via a wireless communication network, and information is fed back to the controller system through sensors, thus constructing a networked two-wheeled robot control system (NCSs). The kinematic model of the two-wheeled robot is described as follows: in, and These represent the linear velocity and angular velocity of the two-wheeled robot, respectively. Disturbances are represented by vectors; the robot's behavior is expressed as a vector. express.

3. The two-wheeled robot safety control method for periodic Markov DoS attacks as described in claim 1, characterized in that, The robot's goal is to track the following circular trajectory: in, It is the parameter vector of the target trajectory; where and These represent the linear velocity and angular velocity of the tracked trajectory, respectively. and This indicates the coordinates and heading angle of the track being tracked.

4. The two-wheeled robot safety control method for periodic Markov DoS attacks as described in claim 1, characterized in that, To obtain the tracking error system, let: Let the sampling period be The following discrete-time state-space model is obtained through linearization and discretization: in, in It is a given constant.

5. A two-wheeled robot safety control system for periodic Markov DoS attacks, based on the two-wheeled robot safety control method for periodic Markov DoS attacks as described in any one of claims 1-4, characterized in that it comprises: The system construction module is used to build a kinematic model of a two-wheeled robot. It integrates and fuses the kinematic model and system signals of the two-wheeled robot through a communication network to build a networked two-wheeled robot control system (NCSs). The linearization and discretization module is used to linearize and discretize the networked two-wheeled robot control system (NCSs) to obtain a discrete-time linear state-space model and construct the motion target of the two-wheeled robot. The security control module is used to determine the type of attack. Utilizing switching system theory, the networked two-wheeled robot control system (NCSs) under attack is transformed into a cyclic Markov system with modal dwell time. A controller is set up, and based on the subsystem constraints of the switching system, its control gain is calculated to control the two-wheeled robot and track the target trajectory of the two-wheeled robot, thereby achieving security control of the networked two-wheeled robot system subjected to periodic Markov DoS attacks.

6. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the two-wheeled robot safety control method for periodic Markov DoS attacks as described in any one of claims 1-4.

7. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform the two-wheeled robot safety control method for periodic Markov DoS attacks as described in any one of claims 1-4.

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